Showering is not required. In my experience, if you do that run at 15mph, it'll take 12 minutes and you'll need to shower and change. If you do it at 12mph, it'll take 15 minutes and you'll be fine in work clothes. Take it slowly, take a few minutes longer riding and arrive sweat-free.

I had a 10 mile commute. Pushing hard, it would take me about 36 minutes and then need 5 minutes to recover, then the shower and change. Taking it easy would be about 5 minutes longer riding-time, but it was a breeze.

i did my first commute yesterday.....7 1/2 miles one way.....not really sweating enough to warrant a shower averaged 13 mph...took me 34 minutes....doubt you would even get warm at that speed....go for it, it will wake you up before your days work. As for the clothes, drive in on a Monday with the weeks supply so you can ride in the rest of the week....then take a detour on the way home to up the miles

Just take it easy on the way in and you won't need a shower. I cycle a similar distance in my work clothes, trousers tucked into socks, sorted. Crawling along at 10-12mph isn't any more taxing than walking really. You can then blast home after work to get a good workout.

Yeah definitely go for it, there are, apart from the obvious financial benefits, a feelgood factor and 5 x 6 is an extra 30 miles a week towards fitness
If you set off at the same time you'd set off driving and bomb it on the bike you will probably arrive earlier than you would in the car so plenty of time to tidy yourself up
Or just take the other advice, nice and steady.. no sweat

My commute is 1.92 miles there and 1.95 home. I've been doing it for just over a year now, and it has worked out very well. I commute in work trousers, tucked into my socks and work shoes. I wear a t-shirt in though, carrying my shirt in a bag and wash and change into my shirt at work. I also have waterproof trousers and overshoes.

It is a different mindset altogether though. I had been cycling seriously about 6 months before I started commuting. Despite being quite regular, and cycling in some terrible weather conditions, there was always a feeling that I was doing it because I wanted to. After I started commuting it took a while to get my head around the fact that I had to do it.

No, just spend money on bike kit rather than petrol. I expect folks who don't get the n+1+1+1 bug who commute into London say and don't run a car probably do save money, especially if a reasonable distance where a season ticket is 2k+ a year